A new theory of precipitator efficiency

Abstract

This paper contains a new theory of precipitator efficiency, designed to avoid certain objections to the Deutsch formula. Its essential concept is that random motions of particles give rise to a directed flow if a concentration gradient exists. Furthermore, the flow tends to smooth out the distribution of particles. Application of this concept to the transverse components of particle velocity leads to a proof that the net velocity of particles towards electrodes is less than the purely electrostatic velocity by a factor (1 − f), where f is the ratio of rate of turbulent transport away from the electrodes to electrostatic transport towards them. The derivation utilizes only the observation that industrial scale precipitators do not achieve laminar efficiencies. Similar considerations for the longitudinal motion show that, in a precipitator, the mean particle velocity exceeds the mean gas velocity. The resultant effection precipitator efficiency depends on the gas velocity: for high velocities, it is relatively unimportant; at low velocities, it becomes more important. On this basis, the decline of effective migration velocity with falling gas velocity, which has been noted in the literature, finds its explanation. Another way of looking at the new theory is the following. For high gas velocities, the efficiency of a precipitator may be calculated by a formula of the same form as that of Deutsch, except that the electrostatic velocity w must be replaced by (1 − f) w. This last quantity corresponds to the effective migration velocity which has been used heretofore on an empirical basis. Thus, the new formula is more pessimistic than the old. At low gas velocities, a new factor, the particle diffusion coefficient, enters into the efficiency calculation in such a way that a significant advantage for low turbulence precipitators is seen. The major differences between the new theory and the old are the introduction of effective migration velocity in a natural manner without special assumptions, and the correlation of efficiency with degree of turbulence.